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Abstract:
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Changes in connectivity of biological networks have been found to be associated with onset and progression of complex diseases. In the past decade, various methods have been proposed for inferring the network structures from partial correlations among variables. However, such methods do not quantify the uncertainty, and are thus not appropriate in determining whether two networks are different. More recently, research has focused on testing whether partial correlation matrices in two populations are the same. However, qualitative differences in network connectivity structures cannot be answered by such methods. In this paper, we propose a novel inference procedure, which tests whether the connectivity of two networks is qualitatively different. Our inference procedure also enables us to draw conclusions on which specific node, if any, shows different connectivity. We use numerical experiments to examine. These experiments show that our method could control the error rate at desired level, and is powerful in identifying qualitative differences in network structure. We demonstrate our procedure in detecting differences in brain networks of trauma patients and healthy individuals.
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